Second-order Slip Condition Research Articles

Important of Slip Effects in Non-Newtonian Nanofluid Flow with Heat Generation for Enhanced Heat Transfer Devices

In various fields such as engineering, nanotechnology, and biomedical sciences, the study of non-Newtonian nanofluid flow with heat generation is becoming increasingly important. However, it is challenging to accurately model such flows due to their complex behavior and slip effects at the fluid-solid interface. This research investigates the impact of first and second-order slip conditions on the flow and heat transfer properties of a non-Newtonian nanofluid using a power law model to describe the fluid's non-Newtonian behavior and numerical methods to solve the resulting equations. To determine the influence of various parameters such as slip parameters, Brinkman number, power law index, and Eckert number on the velocity, temperature, and concentration profiles, which this study examines. The study shows that slip parameters significantly determine the flow and heat transfer properties of non-Newtonian nanofluids, the study also reveals that slip parameters are a crucial factor in understanding the flow and heat transfer characteristics of nanofluids, with the second-order slip condition having a greater impact on velocity and temperature profiles than the first-order slip condition. These findings are valuable for developing and optimizing heat transfer devices that involve non-Newtonian nanofluids with heat generation, which is essential for technological advancements in today's industry.

Investigation of radiative MHD Carreau nanofluid over an inclined stretching cylinder with activating energy, Wu’s slip, and convective heating

The influence of radiation, convective heating, second-order velocity slip condition, and activating energy on the magnetohydrodynamic (MHD) Carreau nanofluid and heat/mass transfer are depicted in this study. A mathematical model of the Carreau nanofluid is carried out with the effects of thermophoresis and Brownian motion. The governing equations are transformed into a system of nonlinear coupled differential equations. Solutions of the transformed equations are derived by the Matlab BVP4c solver. Efficiency of the solver is verified by the comparison with the previous literature. Moreover, the impacts of the dimensionless velocity, temperature, and nanoparticle concentration profile are elucidated graphically.

Parametric simulation of hybrid nanofluid flow consisting of cobalt ferrite nanoparticles with second-order slip and variable viscosity over an extending surface

Abstract This study explores the unsteady hybrid nanofluid (NF) flow consisting of cobalt ferrite (CoFe2O4) and copper (Cu) nano particulates with natural convection flow due to an expanding surface implanted in a porous medium. The Cu and CoFe2O4 nanoparticles (NPs) are added to the base fluid water to synthesize the hybrid NF. The effects of second-order velocity slip condition, chemical reaction, heat absorption/generation, temperature-dependent viscosity, and Darcy Forchheimer are also assessed in the present analysis. An ordinary differential equation system is substituted for the modeled equations of the problem. Further computational processing of the differential equations is performed using the parametric continuation method. A validation and accuracy comparison are performed with the Matlab package BVP4C. Physical constraints are used for presenting and reviewing the outcomes. With the increase in second-order velocity slip condition and unsteady viscosity, the rates of heat and mass transition increase significantly with the variation in Cu and Fe2O4 NPs. The findings suggest that the uses of Cu and Fe2O4 in ordinary fluids might be useful in the aerodynamic extrusion of plastic sheets and extrusion of a polymer sheet from a dye.

Second-Order Slip Effect on MHD Flow and Radiative Heat Transfer through Porous Medium due to an Exponentially Stretching Sheet

The magnetohydrodynamic (MHD) boundary layer flow and radiative heat transfer with second-order slip condition are investigated in this paper. The fluid flow is considered towards an exponentially stretching sheet. The effect of magnetic field and thermal conductivity are taken into account. The obtained nonlinear mathematical expression of the flow are transformed into ordinary differential equations by similarity transformation. The coupled higher order nonlinear ordinary differential equations are solved numerically. The solution for velocity and temperature profile against the first and second-order slip parameters are analyzed. Significant changes are observed in skin friction coefficient and Local Nusselt number due to the magnetic parameter. The characteristics of the flow are discussed through graphs for different pertinent parameters. The results designate that the Local Nusselt number reduces with the increased value of magnetic parameter but opposite behavior is observed for the skin friction coefficient. The rate of heat transfer decreases with higher value of Prandtl number and enhances for Radiation parameter.
 HIGHLIGHTS
 
 Phenomenon of an exponentially stretching sheet with thermal conductivity also incorporate in fluid flow
 Behavior of magnetic parameter (M) and Radiation parameter (R) are analyzed
 Highly nonlinear mathematical equations are solved numerically
 Variation of velocity profile obtained for the first and second order slip parameters
 
 GRAPHICAL ABSTRACT

Improved curved-boundary scheme for lattice Boltzmann simulation of microscale gas flow with second-order slip condition

An improved curved-boundary scheme with second-order velocity slip condition for multiple-relaxation-time-lattice Boltzmann (MRT-LB) simulation of microgas flow is proposed. The proposed interpolation bounce-back (IBB)-explicit counter-extrapolation (ECE) scheme adopts the IBB method to describe the curved boundary, while the ECE method is employed to predict the slip velocity on gas-solid interface. To incorporate the effect of second-order velocity slip term and the influence of boundary curvature, a slip velocity model is also derived, from which the gas slip velocity is captured by the ECE discretization method. The influence of fictitious slip velocity can be eliminated by adopting the present ECE method, and the influence of actual offset between the lattice node and the physical boundary can be well considered by the IBB method. The proposed IBB-ECE boundary scheme is then implemented with the MRT-LB model and tested by simulations of force-driven gas flow in horizontal (inclined) microchannel, gas flow around a micro-cylinder, and Couette flow between two micro-cylinders. Numerical results show that the proposed IBB-ECE scheme improves the computational accuracy of gas slip flow (0.001<Kn≤0.1) when compared with other boundary schemes reported in the literature, and provides a precise and easy implementing scheme for curved boundary with second-order slip condition.

Chemical entropy generation and second-order slip condition on hydrodynamic Casson nanofluid flow embedded in a porous medium: a fast convergent method

The chemical entropy generation analysis is an approach to optimize the performance of different thermal systems by investigating the related irreversibility of the system. The influences of second-order slip with the chemical reaction on the boundary layer flow and heat transfer of a non-Newtonian nanofluid in a non-Darcian porous medium have been investigated numerically. Simultaneous solutions are presented for first and second-order velocity slips. The second-order boundary conditions serve as a closure of a system of the continuity, transport, and energy differential equations. The current work differs from the previous studies in the application of a new second-order slip velocity model. The Casson fluid model is applied to characterize the non-Newtonian fluid behavior. The effect of the second slip parameter on the present physical parameters was discussed through graphs and it was found that this type of slip is a very important one to predict the investigated physical model. The present study provides two fast convergent methods on the semi-infinite interval, namely Chebyshev collocation method and optimal homotopy analysis method are used to analyze the fluid flow, heat, and mass transport. Compared with available analytical and numerical solutions, current methods are effective, quickly converging, and with great accuracy. It was shown that the account for the second-order terms in the boundary conditions noticeably affects the fluid flow characteristics and does not influence on the heat transfer characteristics.

CONVECTIVE FLOW OF PRANDTL HYBRID NANOFLUID (SWCNT-MWCNT/EG) OVER AN EXPONENTIALLY ELONGATED SHEET WITH SECOND-ORDER SLIP

: Background: Recently, in many engineering (power generation, biosensors) and industrial (oil refineries, medical equipment) systems hybrid nanofluids are used to advance the competence of their energies and cooling techniques. These nanoparticle combinations are less damaging to the equipment and act as an environmentally friendly agent for saving energy. In this paper, carbon single-wall nanotubes (SWCNT) and multiwall carbon nanotubes (MWCNT) are considered as a nanoparticles and Ethylene glycol (EG) as a abase fluid. The convective flow of Prandtl hybrid nanofluid (SWCNT-MWCNT/EG) past an exponential elongated surface with second-order slip condition is investigated in this paper using a simplified mathematical model. Method: By using similarity transformations, the governing equations in the current study are turned into a highly nonlinear system of ODEs and are solved by using an integrated shooting scheme. Results: The effects of selected parameters on velocity, fluid temperature, heat transfer rate, and skin friction factor are discussed graphically for both nanoparticles. It is established that the heat transfer rate enhances with an increase in the Biot number and Prandtl number. Also, the fluid momentum with the first-order slip condition is more than that of the second-order slip.

Dual Solutions of EMHD Nanofluid at Stretching Sheet with Mixed Convection Slip Boundary Condition

In this paper stagnation boundary layer flow of nanofluid with mixed convection heat and mass transfer with Electrical Magneto Hydrodynamic (EMHD) effects over a second-order momentum slip boundary condition have been mathematically analysed. The governing equations are transformed by similarity variable and the problem becomes coupled third-order nonlinear coupled differential equations. We use fourth-order Runge Kuta method and shooting technique to find the solution. The effect of second-order momentum slip condition with linear thermal slip condition has determined. Variation of all nano energy conversion parameters depends on different factors has shown graphically. Some of the parameters possesses dual solution at different values of second-order velocity slip parameter (β1&amp;β2).

Influence of Chemical Reaction and Arrhenius Activation Energy on Hydromagnetic Non-Darcian Casson Nanofluid Flow with Second-Order Slip Condition

This article investigates the combined effect of second-order velocity slip, Arrhenius activation energy and binary chemical reaction on reactive Casson nanofluid flow in a non-Darcian porous medium. The governing equations of the problem were first non-dimensionalized and later reduced to ordinary nonlinear differential equations by adopting a similarity transformation. The emerging nonlinear boundary value problem was solved by using Galerkin weighted residual method (GWRM). The obtained results were compared with those found in the literature to validate our method. The impact of pertinent parameters on the velocity component, temperature distribution and concentration profile are presented using graphs and were discussed. The computational results show that an increase in second order slip parameter significantly results to an increase in the temperature as well as nanoparticle concentration profiles, while it reduces the velocity profile.

Effects of Second-Order Slip Flow and Variable Viscosity on Natural Convection Flow of CNTs − Fe 3 O 4 /Water Hybrid Nanofluids due to Stretching Surface

This study deals with natural convection unsteady flow of CNTs − Fe 3 O 4 /water hybrid nanofluids due to stretching surface embedded in a porous medium. Both hybrid nanoparticles of SWCNTs − Fe 3 O 4 and MWCNTs − Fe 3 O 4 are used with water as base fluid. Effects of hybrid nanoparticles volume friction, second-order velocity slip condition, and temperature-dependent viscosity are investigated. The governing problem of flow is solved numerically employing spectral quasilinearization method (SQLM). The results are presented and discussed via embedded parameters using graphs and tables. The results disclose that the thermal conductivity of CNTs − Fe 3 O 4 / H 2 O hybrid nanofluids is higher than that of CNTs − H 2 O nanofluids with higher value of hybrid nanoparticle volume fraction. Also, the results show that momentum boundary layer reduces while the thermal boundary layer gros with higher values of temperature-dependent viscosity and second-order velocity slip parameters. The skin friction coefficient improves, and the local heat transfer rate decreases with higher values of nanoparticle volume fraction, temperature-dependent viscosity, and second-order velocity slip parameters. Furthermore, more skin friction coefficients and lower local heat transfer rate are reported in the CNTs − Fe 3 O 4 / H 2 O hybrid nanofluid than in the CNTs − H 2 O nanofluid. Thus, the obtained results are promising for the application of hybrid nanofluids in the nanotechnology and biomedicine sectors.

Effects of Second-Order Velocity Slip and the Different Spherical Nanoparticles on Nanofluid Flow

The paper theoretically investigates the heat transfer of nanofluids with different nanoparticles inside a parallel-plate channel. Second-order slip condition is adopted due to the microscopic roughness in the microchannels. After proper transformation, nonlinear partial differential systems are converted to ordinary differential equations with unknown constants, and then solved by homotopy analysis method. The residual plot is drawn to verify the convergence of the solution. The semi-analytical expressions between NuB and NBT are acquired. The results show that both first-order slip parameter and second-order slip parameter have positive effects on NuB of the MHD flow. The effect of second-order velocity slip on NuB is obvious, and NuB in the alumina–water nanofluid is higher than that in the titania–water nanofluid. The positive correlation between slip parameters and Ndp is significant for the titania–water nanofluid.

FRACTAL MODELS FOR GAS–WATER TRANSPORT IN SHALE POROUS MEDIA CONSIDERING WETTING CHARACTERISTICS

Complicated gas–water transport behaviors in nanoporous shale media are known to be influenced by multiple transport mechanisms and pore structure characteristics. More accurate characterization of the fluid transport in shale reservoirs is essential to macroscale modeling for production prediction. This paper develops the analytical relative permeability models for gas–water two-phase in both organic and inorganic matter (OM and IM) of nanoporous shale using the fractal theory. Heterogeneous pore size distribution (PSD) of the shale media is considered instead of the tortuous capillaries with uniform diameters. The gas–water transport models for OM and IM are established, incorporating gas slippage described by second-order slip condition, water film thickness in IM, surface diffusion in OM, and the total organic carbon. Then, the presented model is validated by experimental results. After that, sensitivity analysis of gas–water transport behaviors based on pore structure properties of the shale sample is conducted, and the influence factors of fluid transport behaviors are discussed. The results show that the gas relative permeability is larger than 1 at the low pore pressure and water saturation. The larger pore pressure causes slight effect of gas slippage and surface diffusion on the gas relative permeability. The larger PSD fractal dimension of IM results in larger gas relative permeability and smaller water relative permeability. Besides, the large tortuosity fractal dimension will decrease the gas flux at the same water saturation, and the surface diffusion decreases with the increase of tortuosity fractal dimension of OM and pore pressure. The proposed models can provide an approach for macroscale modeling of the development of shale gas reservoirs.

Correction of second-order slip condition for higher Knudsen numbers by approximation of free-molecular diffusion

The computational predictions of channel and pipe flows with classical models and no-slip condition at the wall reach excellent results for lower Knudsen numbers (Kn) only. Linear slip models reach a very good approximation of measurement results over the region of 10−3 &amp;lt; Kn &amp;lt; 10−1. The numerical results of higher-order slip models match experimental data up to Kn ≈ 1. The present work derives an analytical model for the transition from the slip regime to the free-molecular flows by the superposition of diffuse molecular boundary reflection and the molecular diffusion inside the bulk flow. The methodology of the present publication models the mass flow resulting from the molecular diffusion for the approximation of the mass flow in microchannels and micropipes for the regime of molecular mass flows (1 &amp;lt; Kn &amp;lt; 100) in an excellent way. The present model shows good agreement with the former models, measurement data, and direct simulation Monte Carlo results for the complete region from the transitional regime up to free-molecular flow (10−2 &amp;lt; Kn &amp;lt; 102).

Pressure Drop and Flow Development in the Entrance Region of Microchannels With Second-Order Velocity Slip Condition and the Requirement for Development Length

AbstractIn this investigation, Lfd* and Δp in the entrance region of circular and parallel plate microchannels have been determined for 10−2≤Re≤104 and 10−4≤Kn≤0.2, employing the second-order velocity slip condition at the wall with C1=1 and 0≤C2≤0.5. Results indicate that although local velocity slip at the wall is always higher than that for the fully developed section, local wall shear stress for higher Kn and C2 could be lower than its fully developed value, which is also more prominent for lower Re. Therefore, depending upon the operating condition, K(x) and Kfd could assume negative values, implying that pressure gradient in the developing region could even be less than that in the fully developed section. It has been further observed that both Lfd* and Kfd are characterized by the low and the high Re asymptotes, using which extremely accurate correlations have been proposed for both geometries.

Second-order slip condition considering Langmuir isothermal adsorption for rarefied gas microflows

Effect of the slip boundary condition on rarefied gas flow simulations plays an important role to understand the behaviour of gas microflows in MEMS. Several second-order slip conditions were proposed by the models of the kinetic theory of gases to simulate the rarefied gas microflows, in which the so-called classical second-order slip condition was derived from the Karniadakis et al. model. In this paper, a new second-order slip condition is proposed to employ with the Navier-Stokes-Fourier equations for simulating the rarefied gas flows in microchannels. It is derived by combining the Langmuir isothermal adsorption and the Karniadakis et al. model, with the aim of achieving a more realistic physical model. The pressure-driven back-forward-step, the Couette and pressure-driven Poiseulle rarefied gas flows in microchannels are investigated to validate our new second-order slip condition. Slip velocities using our new second-order slip condition are better than those using the conventional Maxwell and the so-called classical second-order slip conditions, and are in very good agreement with the DSMC data for all cases considered.

Second-order slip condition considering Langmuir isothermal adsorption for rarefied gas microflows

Second-order slip condition considering Langmuir isothermal adsorption for rarefied gas microflows

Effect of second order slip condition on the flow of Tangent hyperbolic fluid—a novel perception of Cattaneo–Christov heat flux

The present exploration aims to analyze the impacts of mass transfer on the flow of Tangent hyperbolic fluid in the process of heat transfer assimilated with relaxation time in the heat flux to attain the state of equilibrium. The improved novel idea of Cattaneo–Christov heat flux instead of the conventional model based on classical heat flux phenomenon is instigated. The flow is subjected to homogeneous and heterogeneous reactions and second-order slip condition past a permeable stretched surface. A dimensionless system of ordinary differential equations by using meaningful transformations is obtained which is solved numerically by Runge–Kutta–Fehlberg Method (RKF45) technique. The upshot of physical quantities versus involved distributions is also given. It is comprehended that the Power law index and the Weissenberg number have opposing effect on velocity profile. Further, the concentration profile is diminishing function of homogeneous and heterogeneous reactions. To corroborate our presented results, an excellent harmony with an already established result in the literature is also achieved.

Impact of Magnetic Field and Second-Order Slip Flow of Casson Liquid with Heat Transfer Subject to Suction/Injection and Convective Boundary Condition

The present article is planned theoretically to throw light on non-Newtonian Casson liquid flow and heat transport analysis over an exponentially stretching sheet with second-order velocity slip condition. The analysis of magneto-hydrodynamic (MHD) is an important interdisciplinary field. One of the most imperative applications related to engineering problems is plasma confinement, liquid-metal cooling of nuclear reactors, and electromagnetic casting. The flow here is considered to be electrically conducting. The modelled equations of mass, momentum and energy transport are reduced into the nonlinear ordinary differential equations by employing a similarity approach which are then solved numerically by employing finite difference collocation process (a three-stage Lobatto IIIa scheme). The inspiration of convergence flow parameters on dimensionless velocity, temperature have been discussed graphically. The obtained results confirm that an excellent agreement is achieved for the Newtonian case with those available in the literature. Consequences establish that skin friction rises in the presence of Casson fluid parameter and the Nusselt number show enhancement for second order slip parameter.

Outlining the impact of second-order slip and multiple convective condition on nanofluid flow: A new statistical layout

An analysis exploring the influence of second-order slip mechanism on nanofluid flow passing over a permeable stretching surface is investigated. Additionally we have captured the flow features including the presence of realistic thermal and solutal boundary conditions. Applying the similarity transformation procedure leads us to convert the partial differential flow related equations into nonlinear ordinary ones. After that we solved them numerically using the fourth-order Runge–Kutta method in conjunction with the shooting technique. Parametric study has been performed through tables and diagrams to highlight the consequence of velocity, temperature, and concentration profile. Moreover, a statistical attempt is made to illustrate the correlation of physical parameters within the flow system.

Heat transfer of nanofluids considering nanoparticle migration and second-order slip velocity

The heat transfer of a magnetohydrodynamics nanofluid inside an annu-lus considering the second-order slip condition and nanoparticle migration is theoret-ically investigated. A second-order slip condition, which appropriately represents the non-equilibrium region near the interface, is prescribed rather than the no-slip condi-tion and the linear Navier slip condition. To impose different temperature gradients, the outer wall is subjected to q2, the inner wall is subjected to q1, and q1 > q2. A modified two-component four-equation non-homogeneous equilibrium model is employed for the nanofluid, which have been reduced to two-point ordinary boundary value differential equations in the consideration of the thermally and hydrodynamically fully developed flow. The homotopy analysis method (HAM) is employed to solve the equations, and the h-curves are plotted to verify the accuracy and efficiency of the solutions. Moreover, the effects of the physical factors on the flow and heat transfer are discussed in detail, and the semi-analytical relation between NuB and NBT is obtained.